Euler and Navier-Stokes equations on the hyperbolic plane

被引：18
|
作者：
Khesin, Boris [1 ,2 ]
Misiolek, Gerard [1 ,3 ]
机构：
[1] Inst Adv Study, Sch Math, Princeton, NJ 08450 USA
[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
[3] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2012年 / 109卷 / 45期
基金：
加拿大自然科学与工程研究理事会;
关键词：
harmonic forms; steady flows; ill-posedness; Dirichlet problem; Dodziuk's theorem; DIRICHLET PROBLEM; INFINITY;
D O I：
10.1073/pnas.1210350109
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane H-2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on H-n whenever n >= 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.
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页码：18324 / 18326
页数：3
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